Assessing the Genetic Diversity of Parents for Developing Hybrids Through Morphological and Molecular Markers in Rice (Oryza sativa L.)

The advancement of hybrid technology plays a crucial role in addressing yield plateau and diminishing resources in rice cultivating regions. The knowledge of genetic diversity among parental lines is a prerequisite for effective hybrid breeding program. In the current study, a set of 66 parental lines was studied for diversity based on both morphological characters and microsatellite SSR markers. The genetic variability parameters unveiled that number of productive tillers per plant, single plant yield and hundred grain weight exhibited additive gene action. Mahalanobis D2 statistics grouped the genotypes into ten clusters based on yield and grain traits. The principal component analysis identified four PCs with eigen value more than one accounting for 71.28% of cumulative variance. The polymorphic SSR markers produced 122 alleles among which the marker RM474 recorded the highest values for Polymorphic Information Content (0.83) and heterozygosity index (0.85). The genotypes were assembled in seven clusters based on jaccard distances using the Unweighted Pair Group method with Arithmetic Mean (UPGMA). The population structure divided the entire population into 3 subpopulations. In both clustering, there was difference in the assembling of genotypes, but, good performing genotypes identified through PCA were positioned in different clusters in both approaches. The genotypes CBSN 495 and CBSN 494 located in different clusters were identified as the potential restorers for high yielding and short duration hybrids. The hybridization among CRR Dhan 310, CRR Dhan 315, IR64 DRT, CB 17135 and WGL 347 can be performed to develop climate smart varieties with improved nutrition. Supplementary Information The online version contains supplementary material available at 10.1186/s12284-024-00691-2.


Background
Rice, filling the calorie requirement of half of the world population faces a challenge marked by yield plateau in the recent years.This challenge compounded with escalating population necessitates urgent focus on increasing productivity which in turn is achieved by developing high yielding hybrids.The success in hybrid breeding largely depends on the genetic diversity of parents used for crossing.This emphasizes the scope of examining genetic diversity among various rice genotypes to help in the selection of precise parents for hybrid breeding.The literatures provide many studies of diversity using both morphological and molecular clustering such as Singh et al. (2022) for 47 rice genotypes, Pathak et al. (2020) for 29 local rice cultivars, Islam et al. (2019) in 28 restorer lines, Vengadessan et al. (2016) for 33 traditional and 12

Introduction
Rice stands as a global significant crop nourishing more than 50% of the world's population (Muthayya et al. 2014).With the demographic expansion under ever declining resources, there is an urgent need to harness heterosis in crop plants.In case of rice, a highly selfpollinated crop, the study of genetic diversity assumes a critical role in the selection of diverse parents aimed for attaining maximum heterosis and transgressive segregants in the successive generations.The understanding of diversity among genotypes is achieved through various multivariate statistical analysis.Mahalanobis D 2 statistics is a potent statistical tool to quantify the genetic distance between genotypes based on replicated data of multiple variables (Mahalanobis 1936).The Principal Component Analysis helps in streamlining the selection process by condensing the total number of variables into key variables with major contribution to the total variation (Devasena et al. 2023;Sheela et al. 2020).The advent of molecular markers enabled the characterization of genotypes more precisely at DNA level differences free from the interference of environmental interactions.The microsatellite Simple Sequence Repeat markers exhibit great level of allelic polymorphism and has widespread application in rice for various molecular studies (Rahman et al. 2011).Further the resolution of population into distinct subgroups is made possible through structure analysis.Assessing the genetic diversity among genotypes based on molecular markers ensure enhanced resolution and significant time savings compared to traditional morphological study.In this regard, the present study was undertaken to assess the genotypic diversity among 66 rice parental lines, employing both morphological and molecular based clustering.The findings aim to provide valuable insights into the significance of these diverse genotypes in the context of rice breeding, offering opportunities for the development of high yielding hybrids to meet the ever-growing global demand.

Materials and Methods
A total of 66 parental lines including released varieties from Tamil Nadu, Andhra Pradesh, Telangana, improved varieties for nutrition and abiotic stress tolerance, indicajaponica cross derivatives in which indica lines were confirmed for restorer genes and wild rice Multi-parent advanced generation inter-cross (MAGIC) derivatives were evaluated at Paddy Breeding Station, Tamil Nadu Agricultural University, India.The station is located at 11 0 N latitude and 77 0 E longitude with an elevation of 426.72 meters above the sea level.The experiment was carried out in Rabi, 2022 in Randomized Block Design with three replications.The list of genotypes with their geographical origin and subspecies type are presented in Table 1.The 30 days old seedlings were transplanted with a spacing of 20 × 20 cm.The fertilizer application and intercultural operations were carried out as per the recommended standard.The observations for ten agronomical and grain traits viz., days to 50% flowering (DFF), plant height (PH), number of productive tillers per plant (NPTP), panicle length (PL), flag leaf length (FLL), single plant yield (SPY), hundred grain weigh (HGW), grain length (GL), grain breadth (GB), grain L/B ratio (L/B) were randomly recorded in 5 plants of each genotype in each replication.The mean values of the genotypes for all the recorded traits are given in Table S1.

Molecular Assay
The Genomic DNA was extracted from young leaf samples of 3-4 weeks old seedlings following Doyle and Doyle's protocol (1987).The Polymerase Chain Reaction (PCR) was performed in a 10 μl reaction mixture: Template DNA 2 μl (20ng/μl), forward primer 0.5 μl (10μM), reverse primer 0.5 μl (10μM), master mix 4 μl (2X) and sterile water (3 μl) for 51 SSR primers distributed across all the chromosomes.The temperature profile used for PCR was initial denaturation at 95 °C (5 min) followed by 35 cycles of denaturation at 94 °C (1 min), annealing at 55 °C (45 s), extension at 72 °C (30 s) and a final extension at 72 °C (10 min).The samples were then held at 4 °C until retrieval.The resulting amplified products were separated on a 3% polyacrylamide gel in 1X TBE buffer alongside a 100 bp ladder (Bio-Helix), visualized under UV transillumination by Bio-Rad imaging system.The details of polymorphic markers along with range of amplified base pair are given in Table 2.The 30 polymorphic primers were scored as '1' and '0' for the presence or absence  1 The list of genotypes with their geographical origin and subspecies type of alleles respectively in all the 66 genotypes.The Jaccard distance based molecular cluster analysis was performed using this scoring while base pair scoring was applied for structure analysis.

Statistical Analysis
The Genetic variability parameters, Analysis of Variance and Principal Component Analysis were performed using the packages 'variability' , ' Agricolae' , 'FactoMineR' and 'factoextra' of R studio 4.2.3.The Mahalanobis D 2 statistics and clustering by Tocher's method was done in TNAUSTAT software (Manivannan 2014).The marker scorings were analysed with R-shiny based package 'PBPERFECT' (Allan 2023) for Jaccard distance, molecular cluster, PIC value and Heterozygosity index.The structure analysis was carried out using STRUCTURE 2.3.4 software and the results were viewed in STRUC-TURE HARVESTER.The Analysis of Molecular Variance (AMOVA), genetic differentiation (Fst), genetic diversity parameters viz., observed heterozygosity (Ho) and expected heterozygosity (He) were analysed using GenAlex 6.5 (Peakall and Smouse 2007).

Genetic Variability
The Phenotypic Co-efficient of Variation (PCV), Genotypic Co-efficient of Variation (GCV), broad sense heritability and Genetic Advance as per cent of Mean (GAM) were calculated for all the traits under study.The estimates of PCV were more than GCV for all the traits indicating the influence of environment in the expression of the traits (Fig. 1).High PCV and GCV were observed for number of productive tillers per plant (33.30, 21.01), single plant yield (49.03, 44.40) and hundred grain weight (21.79, 21.13).All other traits except grain length exhibited low range for both PCV and GCV.The range of heritability and GAM was derived between moderate to high for which the traits viz., days to 50% flowering, plant height, number of productive tillers per plant, single plant yield, hundred grain weight, grain breadth and grain length breadth ratio had high heritability coupled with high GAM.These traits offer advantage by responding to selection and therefore can be taken as a criterion for selection of parents.

Morphological Diversity
The Analysis of Variance (ANOVA) for the ten biometrical traits revealed significant variation among all the genotypes (Table 3).The genetic diversity of parental lines was estimated by Mahalanobis D 2 statistics and the genotypes were categorized into clusters by Tocher's method.All the 66 genotypes were grouped into ten clusters based on D 2 values in a random manner without any consideration of origin or subspecies (Table 4).The cluster I was the largest comprising 19 genotypes followed by cluster IV (10 genotypes).The clusters V, III, II and VI contained 9, 7, 6 and 2 genotypes respectively.The clusters VII, VIII and X contained 4 genotypes in each and cluster IX was identified as a solitary cluster with only one genotype viz., CBSN 495.The intra and inter cluster distances (Table 5) portray the diversity within and among the different clusters respectively.The maximum inter cluster distance was recorded between clusters III and X (5952.26)followed by clusters VIII and X (4915.97)and clusters IX and X (4259.24).The cluster X comprised of wild rice magic derivatives therefore it was showing maximum diversity with most of the other clusters.The minimum inter cluster distance was observed between clusters I and IV (197.00)followed by clusters II and VI (215.24)emphasizing close relation between them.The maximum intra cluster distance was observed for cluster VII (175.97)followed by cluster X (158.30) and cluster IV (153.66).The minimum intra cluster distance was noticed for cluster IX (0) since it was solitary with single genotype followed by cluster III (102.85).The trait days to 50% flowering (79.63%) exerted maximum contribution

S.
No.

Marker Sequence (5'-3')
Chromosome number Annealing Temperature Amplified product size (bp) Table 2 The list of polymorphic markers along with their sequence, chromosome number, annealing temperature and range of amplified product size

RMS-PPR9 − 1 F: G A G T T T T G A A T A G A T T T A C G T G T G G A R: A G T G T C C A G A T T C G T A G T
towards total divergence (Table S2 and Fig. 2).It was followed by hundred grain weight (7.79%), plant height (5.17%), flag leaf length (4.66%) and panicle length (2.75%).This showed that the genotypes had a wide variation with regard to duration.The cluster mean for all the traits are given in    number of productive tillers per plant, panicle length, flag leaf length and low mean value for grain breadth.The genotypes from this cluster shall be employed as parents for producing superior hybrids with medium slender grain type.

Principal Component Analysis
The PCA reduces the dimensionality of data by identifying the most prominent few variables responsible for variation in the genotypes.The principal component analysis for the morphological traits under study revealed the presence of variability among all the parental lines.
The factor loadings of each variable, eigen values, percent of variance and cumulative percent of variance for all the ten principal components are given in Table 7.The first four PCs had eigen value > 1 and accounted for a cumulative variance of 71.28%.PC1 (eigen value of 2.65) contributed 26.48% of total variance followed by PC2 (19.50%),PC3 (14.43%) and PC4 (10.87%).The remaining PCs altogether contributed 28.72% to the total divergence of the genotypes.Days to 50% flowering (0.205), plant height (0.423), panicle length (0.322), flag leaf length (0.247), hundred grain weight (0.425), grain length (0.152) and grain breadth (0.501) exhibited positive weightage to PC axis 1.The PC2 showed positive loadings for days to 50% flowering (0.186) and grain breadth (0.256).In PC3, hundred grain weight (0.321), grain length (0.390) and grain breadth (0.208) and in PC4, days to 50% flowering (0.557) and hundred grain weight (0.213) had positive weightage to the corresponding PC axis respectively.The scree plot (Fig. 3) displaying the relation between all the principal components and the contribution of variation percent depicted the PC1's dominant role in variation among the genotypes guiding trait selection to harness maximum variability.
The degree and the relation between variables are shown as vectors in PCA plot for variables (Fig. 4).The length of the variable vector is directly proportional to the contribution of respective trait to the total divergence.Considering the traits with positive loadings to the first four PCs, the longest vector is observed for grain breadth followed by plant height, hundred grain weight, grain length and panicle length.The maximum contribution by the traits to the total divergence is pronounced

UPGMA Clustering
Thirty Polymorphic Simple Sequence Repeat markers produced a total of 122 alleles among 66 parental lines.
The number of alleles produced per marker ranged from 2 (RM1, RM443, RM471, RM555, RM205 and RM267) to 9 (RM474) with an average of 4 alleles per marker (Table 8).The marker RM474 (Fig. 6) recorded the highest values for Polymorphic Information Content (PIC) (0.83) and heterozygosity index (0.85).Conversely, RM267 had the lowest PIC (0.28) and heterozygosity index (0.33).The average values for PIC and heterozygosity index were 0.55 and 0.61 respectively.The genotypes were assembled in seven clusters based on Jaccard distances (dissimilarity coefficient) using the Unweighted Pair Group method with Arithmetic Mean (UPGMA) (Table S3 and Fig. 7).The largest cluster with 15 genotypes was cluster IV followed by cluster I and III with 11 genotypes each.The cluster VI contained 9 genotypes,

Population Structure
The population structure analysis using Bayesian modelbased approach in STRUCTURE 2.3.4 software was conducted on 66 genotypes.The program was set at 50,000 burns in iterations with number of subpopulations k from 1 to 10.The best k value was determined by plotting likelihood value LnP(D) against ad hoc statistics (Δk) according to Evanno et al. (2005).The maximum value for Δk (10.89) was attained when k = 3 (Fig. 8).Therefore, the entire material was divided into 3 subpopulations (Fig. 9).The second subgroup (SG2) was the largest with 32 genotypes (56.25% pure and 43.75% admixture), followed by first subgroup (SG1) with 16 (62.5% pure and 37.5% admixture) and third subgroup (SG3) with 18 genotypes (55.56% pure and 44.44% admixture) respectively.
The Analysis of Molecular Variance (AMOVA) delineated the total genetic variation, revealing that 80% of the variation existed among individuals within populations.
The genetic divergence among populations accounted for 16%, while variation within individuals contributed 4% to the total variation (Table 9, Supplementary figure 1).On examining pairwise genetic differentiation (Fst) between subpopulations, SG2 and SG3 registered large divergence (0.171) which suggested limited gene flow between them as corroborated by the lowest Nm value of 1.212 (Table 10).The overall average Fst and Nm for the populations were 0.159 and 1.321 respectively.The quantification of genetic diversity parameters identified SG1 and SG2 with highest expected and observed heterozygosity (0.563, 0.036) respectively.SG3 displayed lowest estimates for both expected and observed heterozgosity (0.485, 0.015).The clusters formed in STRUC-TURE analysis were not in congruent with biometrical clustering which were evident through the disparity in the number of clusters formed based on molecular and morphological data.In the morphological clusters, there was a co-mingling of genotypes representing both indica and indica-japonica derivatives.In contrast, the population structure analysis conducted through STRUC-TURE distinctly categorized the subspecies, allocating all indica-japonica cross derivatives to SG3, while genotypes The numbers denote genotypes* and the vectors correspond to the biometrical traits The genotypes are numbered according to the list provided in Table 1 belonging to the indica subspecies were segregated into SG1 and SG2.Furthermore, the grouping of all improved varieties in a single subgroup (SG2) in STRUCTURE contrasts with their disparate placement across different clusters in the D 2 grouping.This discrepancy may be attributed to environmental and seasonal influences, which are known to impact morphological clustering.

Discussion
In the light of surging global population and depleting resources, it is crucial to explore alternatives that enhance the productivity of rice in major regions worldwide.This necessitates a shift towards leveraging heterosis to overcome the challenges posed by the yield plateau of existing varieties.A deep understanding of the genetic diversity among parental lines is essential for optimizing hybrid breeding outcomes.With this goal, we initiated an investigation involving 66 rice genotypes to assess the genetic landscape and provide insights for the judicious selection of parents in effective hybrid breeding.
The study of genetic parameters revealed that PCV was more than GCV which indicated the influence of environmental parameters other than genes in the determination of phenotype.The number of productive tillers per plant, single plant yield and hundred grain weight had high PCV, GCV, heritability and genetic advance.The traits days to 50% flowering, plant height, grain length and grain length breadth ratio also possessed high heritability, GAM with moderate GCV.These traits offer wide variability coupled with additive gene action and therefore selection based on these traits is appreciable for choosing parents.Similar report for yield and grain characters were furnished by Duraiswamy et al. (2023) and Khalequzzaman et al. (2023) respectively.In D 2 statistics, the clustering of 66 genotypes in ten different clusters indicated sufficient genetic diversity existing in the experimental material.Most of the released varieties from Tamil Nadu and Andhra Pradesh were grouped together in cluster I while, varieties released from Tamil Nadu were also grouped in cluster II.This clearly indicated that there was no association between genetic diversity and geographical origin.This was in agreement with the findings of Bhargavi et al. (2023), Bhoite et al. (2023) and Srinivas et al. (2023).The distribution of indica-japonica cross derived lines in different clusters (III, IV, V, VI and VII) indicated that artificial selection and genetic drift played a significant role in determining genetic diversity.The grouping of genotypes in cluster V with less intra cluster distance showed close resemblance for days to 50% flowering and could be due to unidirectional selection pressure during development of these genotypes (Srinivas et al. 2023).The maximum intra cluster distance for cluster VII and X shall be explained to be the result of past selection history, degree of combining ability, genetic architecture or the genotype heterogeneity (Dinesh et al. 2023).The maximum contribution of days to 50% flowering, hundred seed weight and plant height to the genetic divergence makes these traits to be the direct selection indices in parental lines.Srinivas et al. (2023Srinivas et al. ( ), jebakani et al. (2023) ) and Jangala et al. (2022) also reported 50% flowering, hundred seed weight and plant height with maximum contribution towards divergence.Based on the cluster mean values, the genotypes in cluster VII (Blue Bonnet/CB 87R 5-3-1, CB 17135, CO 51 Pyr A10, CBSN 500) can be used as donors for producing hybrids with high yield and high panicle length.The genotypes in cluster III (CBSN 499,WGL 347 and WGL 283) can be employed as donors to produce dwarf and early maturing hybrids.The indica-japonica cross derivative CBSN 495 in the solitary cluster shall be employed as a parent in three-line breeding in order to achieve high yield with good restorability of fertile hybrids.The higher inter cluster distances than intra cluster distances express enough genetic variability to be present among the genotypes (Jebakani et al. 2023).On combining high inter cluster distance and cluster mean, the crosses between genotypes in clusters III, IX and cluster V, cluster VII and VI are beneficial to obtain superior hybrids.Principal component analysis (PCA) measures the spatial distance between genotypes, contrasting with D 2 statistics (Nadarajan et al. 2016) 2006) reported lower mean values than our findings for PIC and number of alleles per locus.The most informative marker with the highest PIC value was identified to be RM474.Based on Jaccard distance, the minimum genetic diversity was found among released varieties which shall be attributed to their free gene flow and shared genetic architecture.Among PCA identified good performing genotypes, high dissimilarity coefficients of 0.90 between CRR Dhan 315 and CBSN 494, 0.83 between CRR Dhan 310 and IR64 DRT and 0.85 between CBSN 495 and CB 17135 were registered.These genotypes also belonged to different molecular clusters reinforcing their genetic distinctiveness.In population structure analysis, the best k value was identified to be 3 which was in accordance with the results of Mishra et al. (2019) in 35 germplasm accessions, Nachimuthu et al. (2015) in 192 rice germplasm lines and Upadhyay et al. (2012) in 25 rice varieties.Most of the genotypes with admixtures were identified to be wild rice derivatives and indica-japonica cross derivatives.The admixtures may be due to the constitution of inherited alleles as a result of artificial crossing and hybridization (Yamasaki and Ideta 2013).The analysis of molecular variance identified significant genetic variation of 80% attributed to differences among individuals within the population.This highlighted the presence of ample variation in the genotypes that can be harnessed in breeding programmes.The pairwise Fst values exceeding 0.15 as propounded by Wright (1978) indicated large genetic differentiation.The lower genetic differentiation and high gene flow observed between SG1 and SG2 was postulated to be the consequence of shared evolutionary history of common parents for released and improved varieties, all belonging to indica Fig. 8 The relation between number of subpopulations and Δk Fig. 7 The clustering of parental lines based on jaccard distance subspecies and the exchange of genetic materials across states for breeding.In contrast, SG3 encompassing genotypes from indica-japonica cross derivatives, exhibited a noteworthy and large genetic differentiation from other two subpopulations.The average observed heterozygosity was 0.022 which was lower than the reports of Tarang et al. (2016) and Suvi et al. (2020).This low estimate can be ascertained to the autogamous mode of reproduction in rice.On the other hand, the average expected heterozygosity, estimated at 0.524, aligned with the findings of Nachimuthu et al. (2015).This can be attributed to the exchange of genes among the genotypes resulting in broad spectrum of genetic diversity.Out of 3 subpopulations, SG3 distinctly encompassed all the indica-japonica cross derivatives in which indica lines were confirmed for the presence of restorer genes.This subgroup could be exploited to select good restorers based on mean value for yield attributes.
The comparison of morphological and molecular cluster revealed that the number of clusters and distribution of genotypes in clusters were different in both approaches.This swapping of genotypes might be attributed to the influence of environment and genotype-environment interaction in determining the morphology.Similar pattern of differences in clusters of morphological and molecular marker analysis were reported by Pathak et al. (2020), Rahman et al. (2011), Vengadessan et al. (2016) and Han-Yong et al. (2004).But the good performing genotypes identified through PCA were positioned in different clusters in both clustering which enable us to select diverse parents for producing superior hybrids.

Conclusion
The present experimental material exhibited a wide genetic divergence in both D 2 statistics and Jaccard distance-based analyses.Two lines viz., CBSN 495 and CBSN 494 located in different clusters were identified as the potential donors for short duration hybrids.The cross between WGL 347, CB 17135 and improved varieties viz., CRR Dhan 310 CRR Dhan 315, IR64 DRT assembled in different clusters shall be attempted to develop

Fig. 3
Fig. 3 Scree plot depicting the relation between all the principal components and the contribution of variation percent

Fig. 5
Fig. 5 PCA BiplotThe numbers denote genotypes* and the vectors correspond to the biometrical traits The genotypes are numbered according to the list provided in Table1 . The contribution of days to 50% flowering, plant height, panicle length, flag leaf length, hundred grain weight, grain length and grain breadth for PC1 in our study is supported by the reports ofNachimuthu et al. (2014),Kathare et al. (2023),Duraiswamy et al. (2023) andGupte et al. (2023).The traits occurring together in different principal components with maximum positive contribution viz., days to 50% flowering, hundred grain weight and grain breadth tend to remain together and so prior importance should be given for positive selection of them in breeding programme(Kumari et al. 2023).In PCA biplot, the genotypes viz., CBSN 495, CB 17135, CBSN 494, CRR Dhan 315, CRR Dhan 310 and IR64 DRT which are good performers for yield contributing traits were positioned around the corresponding trait vectors in the same quadrant.The genotype WGL 347, despite high yield appeared in a different quadrant due to low plant height, making it a viable parent.All these genotypes identified in PCA were assembled in the diverse clusters (III, V, VI, VII and IX) by D 2 statistics.The cluster analysis by Jaccard distance for SSR scoring grouped the 66 parental lines into seven clusters.The released varieties from Tamil Nadu, Andhra Pradesh and Telangana were grouped in cluster I and II reflecting similarity in parentage for medium slender grain types preferred in those regions.Bhattacharjee et al. (2021) also reported marker-based grouping independent of geographical origin.The average PIC (0.55) and the number of alleles (4) were in close accordance with the reports ofTripathi et al. (2020) who reported average alleles of 3.7 and average PIC of 0.56 in molecular diversity analysis of 27 rice cultivars using 12 SSR markers and Salem and Sallam (2016) who obtained average values of 4.5 and 0.57 for number of alleles per locus and PIC respectively in genetic diversity study of 22 Egyptian and exotic rice genotypes using 23 SSR markers.Whereas Pandita et al. (2023), Akter et al. (2022) and Bajracharya et al. (

Fig. 9
Fig. 9 Pictorial representation of distribution of parental lines into different subgroups

Table 4
Clustering of genotypes by Tocher's method

Table 6
. The cluster III recorded low mean values for days to 50% flowering (79.05) and plant height (68.52).The high mean values were registered for panicle length (25.50) and single plant yield (28.63) by cluster VII, flag leaf length (32.37) by cluster VI, hundred grain weight (2.57) and plant height (118.33) by cluster IX.The cluster II had comparably high mean values for

Table 5
The inter and intra cluster distances among ten clusters Numbers in bold font -intra cluster distances; numbers in normal font -inter cluster distances

Table 6
The cluster mean for all the biometrical traits

Table 7
The factor loadings, eigen values, percent of variance and cumulative percent of variance for all principal components

Table 8
The list of polymorphic markers along with their number of alleles, Polymorphic Information Content (PIC) value and heterozygosity index

Table 9
Analysis of molecular variance between subpopulations

Table 10
Pairwise genetic differentiation (Fst) and gene flow (Nm) between three subpopulations along with observed and expected heterozygosity Fst values below diagonal and Nm values above diagonal